$J$ $K$ $L$ If: $ JK = 9x + 3$, $ KL = 5x + 2$, and $ JL = 75$, Find $KL$.
Explanation: From the diagram, we can see that the total length of ${JL}$ is the sum of ${JK}$ and ${KL}$ $ {JK} + {KL} = {JL}$ Substitute in the expressions that were given for each length: $ {9x + 3} + {5x + 2} = {75}$ Combine like terms: $ 14x + 5 = {75}$ Subtract $5$ from both sides: $ 14x = 70$ Divide both sides by $14$ to find $x$ $ x = 5$ Substitute $5$ for $x$ in the expression that was given for $KL$ $ KL = 5({5}) + 2$ Simplify: $ {KL = 25 + 2}$ Simplify to find ${KL}$ : $ {KL = 27}$